The New Sudoku Players' Forum

[anathema]

hi folk,

I had a ingredibly hard puzzle with simple forcing loop, xy-wings, swordfish and a comprehensive forcing chain. I think I need some time only to follow the clues ;-)

Shall I post this puzzle here? Is anyone interessted?

I think it's good for learning.

ciao anathema

[MCC]

Welcome Anathema

Please post any puzzle you think is of interest, there're folk here who will be willing to dissect it.

MCC

[anathema]

ok so here is the puzzle:

Code: Select all

 *-----------*
 |...|.3.|.59|
 |4..|..2|...|
 |..2|..6|.1.|
 |---+---+---|
 |..1|3..|..4|
 |...|.5.|...|
 |2..|..7|3..|
 |---+---+---|
 |.9.|4..|6..|
 |...|1..|..8|
 |54.|.7.|...|
 *-----------*


[Lardarse]

That does not look like a fun puzzle to do with just a pencil...

[rubylips]

The puzzle falls fairly quickly to the Almost Locked Set analysis discussed recently in the Solving Techniques section. The tricky stuff starts here:

Code: Select all

 . 1 . | . 3 4 | 2 5 9
 4 . . | . 1 2 | . . .
 . . 2 | . . 6 | 4 1 .
-------+-------+------
 . . 1 | 3 . . | 5 . 4
 . . 4 | . 5 1 | . . .
 2 . . | . 4 7 | 3 . 1
-------+-------+------
 1 9 . | 4 . . | 6 . 5
 . 2 3 | 1 . 5 | . 4 8
 5 4 . | . 7 . | 1 . .

   678     1  67 |    78     3    4 |    2      5    9
     4   357  59 |   579     1    2 |   78   3678  367
  3789  3578   2 |  5789    89    6 |    4      1   37
-----------------+------------------+-----------------
   789   678   1 |     3  2689   89 |    5  26789    4
  3789  3678   4 |  2689     5    1 |  789   6789  267
     2   568  59 |   689     4    7 |    3    689    1
-----------------+------------------+-----------------
     1     9  78 |     4    28   38 |    6    237    5
    67     2   3 |     1    69    5 |   79      4    8
     5     4  68 |  2689     7  389 |    1     39   23


The cells {r9c6,r9c8,r9c9} form an Almost Locked Set, so when r9c9 doesn't contain a 2, r9c6 must contain an 8.

Code: Select all

Consider the chain r7c5-2-r7c8-2-r9c9-<2|8>-r9c6.
When the cell r7c5 contains the value 8, so does the cell r9c6 - a contradiction.
Therefore, the cell r7c5 cannot contain the value 8.
- The move r7c5:=8 has been eliminated.
The value 2 is the only candidate for the cell r7c5.


The next tricky bit is the following:

Code: Select all

 . 1 . | . 3 4 | 2 5 9
 4 . . | . 1 2 | . . .
 . . 2 | . . 6 | 4 1 .
-------+-------+------
 . . 1 | 3 . . | 5 2 4
 . . 4 | 2 5 1 | . . .
 2 . . | . 4 7 | 3 . 1
-------+-------+------
 1 9 . | 4 2 . | 6 . 5
 . 2 3 | 1 . 5 | . 4 8
 5 4 . | . 7 . | 1 . 2

   678     1  67 |    78    3    4 |    2     5    9
     4   357  59 |   579    1    2 |   78   678  367
  3789  3578   2 |  5789   89    6 |    4     1   37
-----------------+-----------------+----------------
    79   678   1 |     3  689   89 |    5     2    4
   389   368   4 |     2    5    1 |  789  6789   67
     2   568  59 |   689    4    7 |    3   689    1
-----------------+-----------------+----------------
     1     9  78 |     4    2   38 |    6    37    5
    67     2   3 |     1   69    5 |   79     4    8
     5     4  68 |   689    7  389 |    1    39    2


The Almost Locked Sets here are {r1c1,r4c1,r8c1} and (trivially) {r4c1,r4c6}. There's an extended link r4c6=8 => r7c6 and r9c6 <>8 => r9c4=8.

Code: Select all

Consider the chain r1c4-8-r1c1-<8|9>-r4c1-<7|8>-r4c6=8=r9c4.
When the cell r1c4 contains the value 8, so does the cell r9c4 - a contradiction.
Therefore, the cell r1c4 cannot contain the value 8.
- The move r1c4:=8 has been eliminated.
The value 7 is the only candidate for the cell r1c4.


Easy from here ...

[behram1506]

hi folk,

I had a ingredibly hard puzzle with simple forcing loop, xy-wings, swordfish and a comprehensive forcing chain. I think I need some time only to follow the clues ;-)

Shall I post this puzzle here? Is anyone interessted?

I think it's good for learning.

ciao anathema

yes iwould love to solve it - i think i can do it in one hour of playing..
behram